By Audun Holme, Robert Speiser
This quantity offers chosen papers as a result of the assembly at Sundance on enumerative algebraic geometry. The papers are unique study articles and focus on the underlying geometry of the subject.
Read Online or Download Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986 PDF
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Additional info for Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986
Contains exactly hO~oc~5-r) ÷ r - I (resp. hO~o C' ÷ r - I ) independant quadrics. iii) The homogeneous ideal of C is generated by quadrics iff the multiplication maps H0wc~5-r) ® HOOc~k) -~ H0coC~5-r*k) (resp. H0~C ' @ HOOc~k) -* H0~c~k) ) are surjective for all k>O. 7: If C is a reduced and irreducible locally Gorenstein curve of arithmetic genus >0, and L is a line bundle generated by its global sections with hO(L)_~5, then the module ~HO(y_ -" L n) is generated, over the ring ~H OLn bV elements of degree i O.
3) above A, B and C are themselves rational 28 linear c o m b i n a t i o n s of CU, TN, TR and the b o u n d a r y c o m p o n e n t s this is e q u i v a l e n t to &0 and Ai, J, Conjecture'. The Picard group of the v ~ r i e t y V of nodal q u r v e s is torsion. The purpose of t h e present p a p e r Is twofold, First, in t h e following sectlon, we will p r o v e t h a t w i t h the exception of the cases g = 0 or ! and 8 = 0 , 1 or 2, the divisor classes A, B, C a n d A a r e indeed independent.
4) a n d t h e p a p e r of Eisenbud a n d Harris . I: Let_C ¢ pr be a curve. If C is s c h e m e theoretically cut out by hv1oersurfaces of deeree e, and if C is contained in s o m e two-dimensional rational normal scroll in pr, then the homogeneous ideal of C is generated by forms of degree ~_ e. R e m a r k : We allow t h e possibility t h a t t h e scroll m a y be singular, a n d r e q u i r e of C only t h a t it be a p u r e l y 1-dimensional s u b s c h e m e . i m a y be applied in several situations.